Mane headed Liverpool in front five minutes after the interval and four minutes later took advantage of a dreadful error by Chelsea keeper Kepa Arrizabalaga as the hosts crumbled.
Liverpool gave new midfield signing Thiago Alcantara a debut off the bench but the Spaniard’s first impact was to offer Chelsea a lifeline by fouling Timo Werner to concede a penalty with a little under 20 minutes remaining.
But Jorginho’s effort was saved by the otherwise redundant Alisson Becker to spare Liverpool any late tension.
Liverpool have won both their opening games while Chelsea have three points.
Harry Kane has been Tottenham Hotspur’s leading marksmen for the last six seasons, but after becoming the first Englishman to make four assists in one Premier League match at Southampton, the Spurs skipper showed there is more to his game than goals.
With Gareth Bale signed to provide further competition for places in the forwards department at Spurs, the current strike force made a real statement in the 5-2 win at St Mary’s.
Son Heung-min will grab the headlines for his four-goal haul and a first Premier League hat-trick, but the quality of the service for Spurs deserves also high praise.
Each Kane assist was impressive in its own right, with the final pass for Son’s fourth the pick of the bunch as he clipped a curling cross into Son’s path on the run without even looking.
“Four amazing assists from Harry, he deserves the man of the match award,” Son said.
“We have been working for five season together now. We know what we like and work hard on our relationship on and off the pitch. Hopefully, there are many more goals to come.”
Spurs manager Jose Mourinho was equally fulsome in his praise.
“In the second half, Harry Kane killed the game, the way he connected the game, the way he was dropping, he allowed Son Heung-min into attacking spaces,” Mourinho said. “His performance was amazing.
“He is man of the match for what he did for the team. Sometimes people think strikers just score goals, but he creates a whole new dynamic that they (Southampton) could not resolve.”
Before the trip to Southampton, Kane, for all his brilliance in front of goal, had provided only eight Premier League assists in the last three seasons.
In comparison to other leading central strikers in the Premier League – Sergio Aguero (17), Jamie Vardy (14) and Pierre-Emerick Aubameyang (11) – that assist return was not impressive.
However, with Son in red-hot form on one side, and Bale determined to make an impression on his return to the Premier League on the other, Kane’s creative talents could become a more regular feature of Tottenham’s play.
Brighton and Hove Albion got their Premier League season up and running with a clinical 3-0 victory over Newcastle United at St James’ Park after an early brace by Neal Maupay.
The Frenchman put Brighton ahead from the penalty spot in the fourth minute when Allan Saint-Maximin brought down Tariq Lamptey after the teenage wing-back cut inside from the right and darted into the box.
Lamptey, 10 days shy of his 20th birthday, was also involved in Brighton’s second three minutes later, releasing Leandro Trossard down the right.
The Belgian fired in a low cross that Maupay slotted home from close range and though the goal was initially disallowed for an offside in the build-up, referee Kevin Friend overturned his decision after consulting the video assistant referee (VAR).
The home side showed more fight after the restart and Callum Wilson spurned Newcastle’s best chance to cut the deficit when he headed over from close range in the 63rd minute after Brighton were caught trying to play out from the back.
Trossard hit the post in the 71st minute before the visitors extended their lead late on when Aaron Connolly curled the ball home after being picked out by Maupay to complete a comfortable win for Brighton.
Leicester City’s victory was also a milestone 100th Premier League win for their manager Brendan Rodgers.
The Foxes top the table, leading a group of five teams on a maximum six points from two games, with a superior goal difference after their opening 3-0 success at promoted West Bromwich Albion.
It was no more than Leicester deserved after falling behind to an early Chris Wood strike, as they displayed a wealth of attacking talent against the battling visitors.